Praise be to Allah.
First, I offer thanks to Allaah for his grace in having guided you to the path of truth after experiencing a dark journey through 'jahiliyyah', a journey into ignorance and meaninglessness. Allaah guides to his truth whomever he wills. At this point of your life, as an expression of gratitude for Allaah's blessing, you should carry out your duties towards him and desist from the actions that gain his wrath. In fact, Allaah, at this point in your life, must take priority over everything else. You further ought to make up for what you missed in the previous part of your life, to double your efforts in performing worship and to haste in doing good deeds.
Secondly, since this lady in question has converted to Islam, thanks to Allaah, none of her kaafir family members can act as a guardian (wali) of her interests; no kaafir can act in this capacity over a Muslim. If there is a Muslim with some authority in your area over the affairs of the Muslim community, then he can act in this capacity, based on the Prophet's (peace be upon him) hadeeth:
"No marriage contract can be concluded without the presence of a Wali. A Sultan (authority figure) can act as a Wali for those without one." (see Ibn Majah and Imam Ahmad, Hadith number 1880; also in Salih al-Jaami', hadeeth number 7556.)
If there is no authoritative Muslim person, then one should refer to the community Muslim leader or any Muslim who is just ('aadil), respected, and of high character, such as the director of the Islamic center or its imam, to conclude the marriage contract of this sister, with her consent.